LAUSR

S-arithmetic inhomogeneous Diophantine approximation on manifolds

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1 Published in 2022 at "Advances in Mathematics"

DOI: 10.1016/j.aim.2022.108239

Abstract: We investigate $S$-arithmetic inhomogeneous Khintchine type theorems in the dual setting for nondegenerate manifolds. We prove the convergence case of the theorem, including, in particular, the $S$-arithmetic inhomogeneous counterpart of the Baker-Sprind\v{z}uk conjectures. The divergence… read more here.

Keywords: diophantine approximation; approximation manifolds; arithmetic inhomogeneous; inhomogeneous diophantine ... See more keywords

A variational principle in the parametric geometry of numbers, with applications to metric Diophantine approximation

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0 Published in 2017 at "Comptes Rendus Mathematique"

DOI: 10.1016/j.crma.2017.07.007

Abstract: Abstract We establish a new connection between metric Diophantine approximation and the parametric geometry of numbers by proving a variational principle facilitating the computation of the Hausdorff and packing dimensions of many sets of interest… read more here.

Keywords: diophantine approximation; parametric geometry; metric diophantine; geometry ... See more keywords

Variants of Khintchine's theorem in metric Diophantine approximation

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0 Published in 2020 at "Journal of Number Theory"

DOI: 10.1016/j.jnt.2020.01.005

Abstract: New results towards the Duffin-Schaeffer conjecture, which is a fundamental unsolved problem in metric number theory, have been established recently assuming extra divergence. Given a non-negative function $\psi: \mathbb{N}\to\mathbb{R}$ we denote by $W(\psi)$ the set… read more here.

Keywords: variants khintchine; psi; diophantine approximation; theorem metric ... See more keywords

DIOPHANTINE APPROXIMATION WITH GAUSSIAN PRIMES

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0 Published in 2019 at "Quarterly Journal of Mathematics"

DOI: 10.1093/qmathj/haz038

Abstract: In this paper we prove that the exact analogue of the author’s work with real irrationals and rational primes (G. Harman, On the distribution of $\alpha p$ modulo one II, Proc. London Math. Soc. (3)… read more here.

Keywords: diophantine approximation; approximation gaussian; mathbb; gaussian primes ... See more keywords

Diophantine approximation by unlike powers of primes

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0 Published in 2017 at "International Journal of Number Theory"

DOI: 10.1142/s1793042117501330

Abstract: Let λ1,…,λ5 be nonzero real numbers not all of the same sign, satisfying that λ1/λ2 is irrational, and η be a real number. In this paper, we prove that for any e > 0 λ1p1… read more here.

Keywords: diophantine approximation; powers primes; unlike powers; approximation unlike ... See more keywords